The Hubble Space Telescope (HST) has recorded evidence of a black hole at the ce

Question

The Hubble Space Telescope (HST) has recorded evidence of a black hole at the center of the M87 galaxy. Using Doppler data, it's been measured that matter is orbiting the center of this galaxy at an orbital speed of 7.5x105 m/s, out at a radius of 5.7x1017 m. Calculate the mass of the black hole at the center of this orbit. If our Sun's mass is 2.0x1030 kg, how many solar masses is this black hole? For comparison, the suspected black hole at the center of our own Milky Way galaxy is estimated to be around 4 million solar masses.

Explanation / Answer

Part A)

Using Kepler's Third Law we can solve this problem. The formula to apply is...

T2 = 42r3/GM

T is the time for one orbit, which can be found by Distance over Velocity. The distance is the circumference of its orbit (2r), so...

T = 2(5.7 X 1017)/(7.5 X 105)

T = 4.775 X 1012 sec

Then

(4.775 X 1012)2 = (42)(5.7 X 1017)3/(6.67 X 10-11)(M)

M = 4.81 X 1039 kg

(Part B)

The number of solar masses is found by

4.81 X 1039/2.0 X 1030

Number = 2.41 X 109 Solar Masses

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